A four-point gap in the race for Champions League qualification is one thing; a four goal victory in a Merseyside derby quite another. Everton have time to bridge the statistical divide with Liverpool in the race for a top-four finish but the psychological blow inflicted by Brendan Rodgers' team will reverberate for much longer. Liverpool's biggest derby win since 1982, their biggest at Anfield since 1972, sent belief in a return to the European elite soaring at Anfield.

"Are you Moyesy in disguise?" sang the Kop as Roberto Martínez, the Everton manager, oversaw an abject visiting performance in which every selection gamble and every shot sailed into a red brick wall. Liverpool were superbly ruthless and humiliated Everton on the counterattack. Steven Gerrard delivered the opening goal and the controlled midfield display he craved, Daniel Sturridge scored twice and Luis Suárez grabbed his 23rd goal of the season as Everton crumbled. Sturridge also missed a penalty and was involved in a brief touchline dispute with Rodgers following his substitution shortly afterwards.

Everton's embarrassment was a credit to Rodgers' tactical nous and the team spirit he has fostered at Liverpool. The game also demonstrated the gulf in quality between the two attacks. Everton had conceded seven league goals since the 3-3 Merseyside derby draw at Goodison Park in November and that tally could have doubled inside 90 minutes at Anfield. Their injury problems are likely to intensify with Romelu Lukaku taken off on a stretcher early on with suspected ankle ligament damage.

Whereas Rodgers' selection calls – Sturridge cutting in from the left and Philippe Coutinho in central midfield – worked to devastating effect, Martínez's gamble on the fitness of Phil Jagielka, Ross Barkley, Antolín Alcaraz and Steven Pienaar misfired badly. Everton's defence was shredded at will during the first half and Liverpool assured themselves of victory inside 14 brutal minutes. It proved the wrong game for Martínez to pair Jagielka and Alcaraz together for the first time in central defence, while poor positional play from John Stones at right-back also added to Everton's problems.

Tim Howard was overworked from the start as Jordan Henderson, Suárez and Sturridge tried their luck from distance and Raheem Sterling was foiled at close range by the USA international. He could not hold out forever and nor could Everton react after a sluggish start, amplified by so many players short of match fitness.

A frenzied pace was not the only similarity with November's derby. All three Liverpool goals in that match arrived from set-pieces, a fact Martínez reminded his team about before the Anfield return, but to no avail.

Rodgers' team took the lead from their first corner when Suárez – pelted with coins from the away section that he handed to referee Martin Atkinson – swept to the near post. Gerrard escaped Gareth Barry's attentions and, with a magnificent leap, steered a powerful header beyond Barkley on the goalline. It was a fitting way for one of the derby's most influential figures to mark a record 28th Premier League appearance in the fixture.

Barry's impact at the corner was not confined to slack marking and, attempting to regain ground on Gerrard, he careered into Lukaku and ended the Everton striker's night. If Martínez thought his problems could not get any worse, he was soon shown to be mistaken.

Coutinho vindicated Rodgers' decision with a piercing pass that sent Sturridge clear of the exposed Stones. He gave Howard no chance with a confident finish that was surpassed by an outstanding lob from Liverpool's next attack two minutes later. The source was painful for the Everton defence, a straightforward clearance from Kolo Touré that sailed over Jagielka and dropped at the feet of Sturridge. The striker had plenty to do but, from the edge of the area, lofted a glorious finish over the stranded keeper and into the net.

Liverpool's fourth was another ordeal for the clearly unfit Jagielka. The Everton captain attempted to cushion a clearance to his central defensive partner but instead found Suárez, the last person in the Premier League who requires an invitation towards goal. The Uruguay international sprinted from the halfway line with Jagielka on his shoulder but reluctant to risk a red card, and Suárez slotted low under Howard to deepen Everton's embarrassment. Jagielka could well be marking Suárez at the World Cup this summer and the only consolation for England is that he should be fit for that encounter.

Only Kevin Mirallas and Barkley continued to carry a threat for the visitors but Liverpool squandered an outstanding chance to make it five before the hour from the penalty spot. Sterling was the latest home player to waltz behind the Everton rearguard and went over as Howard raced from goal. Only the direction of Sterling's run spared the keeper a card and Everton escaped further ignominy when Sturridge took the spot-kick for a derby hat-trick only to blaze over the bar.

Sturridge's decision to go for the hat-trick again later on with Suárez better placed brought a furious response from team-mates. His withdrawal followed – for tactical reasons insisted Rodgers – after a brief exchange of words with the striker. Not that anything could take the gloss from a stunning night for Liverpool.